What is the difference between the sum from (1) to (150) and the sum from (1) to (100)?
Answer and explanation
Correct answer: 6275
The sum of the first 150 natural numbers is \(\frac{150\times151}{2}=11325\), and the sum of the first 100 natural numbers is \(\frac{100\times101}{2}=5050\). Therefore, the difference is \(11325-5050=6275\). Equivalently, it is the sum of the numbers from 101 to 150. A nearby value such as 6175 results from an incorrect calculation. Exam tip: when subtracting two consecutive sums, the remaining terms begin at 101, not 100.
Frequently asked questions
What is the correct answer to this question?
6275
Why is this the correct answer?
The sum of the first 150 natural numbers is \(\frac{150\times151}{2}=11325\), and the sum of the first 100 natural numbers is \(\frac{100\times101}{2}=5050\). Therefore, the difference is \(11325-5050=6275\). Equivalently, it is the sum of the numbers from 101 to 150. A nearby value such as 6175 results from an incorrect calculation. Exam tip: when subtracting two consecutive sums, the remaining terms begin at 101, not 100.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Sum of first n natural numbers.
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